Rendering Cycles and Internal in the same scene without compositing
If you mean without using the compositor at all, then I don't think it can be done in one go, but it should be easy to render one scene and then the other.

If you mean just without combining the Cycles BI renders, then it is possible:

File output node:

This can be done with the File output node.

Setup your 3rd scene's composite nodes like this:



Select the File output node and set the output format to Multilayer EXR. You can add inputs (layers) with the Add input button in the Properties region (N):



So if you wanted you could even put both the BI and cycles renders in one EXR sequence:



When you want to composite you can open the multilayer EXR in an Image node and get all your layers: